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The circle of fifths

The circle of fifths is a graphic representation of the relationships between major and minor keys and their respective key signature.

The circle of fifths

The circle of fifths (or cycle of fifths) is a graphical representation of the relationships between major, minor keys and their respective key signature.

The circle of fifths is a key element in understanding the tonal system. Take the time to read it well, to understand the mechanisms and then try to reproduce it (a practical exercise is dedicated later in this course). If you succeed without consulting the solution, it means you master the subject.

FIGURE 1 - Circle of fifths
dièses bémols

How to read it

The circle of fifths reads like a clock.

At noon, there is the C Major key, which has an empty key signature.

When going clockwise, we add a sharp to the key signature at each clock, following the sharp series. Thus, each time, the key advances from perfect fifth to perfect fifth in the ascending direction (C → G → D → A etc.) hence the name circle of fifths.

When turning counterclockwise, we add a flat at each hour, following the flat series. Here too, we advance from fifth to fifth, but downwards this time.

The meeting of flats and sharps

For the three notches located at the bottom of the circle (equilavent to 5, 6 and 7 o'clock), the flat and sharps keys meet. Indeed, C Major is equivalent to D Major, F Major is equivalent to G Major, and B Major is equivalent to C Major. These keys are called enharmonic keys because, although they are named differently, they proceed from the same harmony.

It is therefore possible to go around the entire circle until returning to C Major.

Enharmonic keys

What is the point of having two writing systems for the same key?

First of all, let's note that a 5-sharp key signature is easier to read than a 7-flat one, as well as a 5-flat signature is easier to read than a 7-sharp one. So we will meet more often the B Major key than that of C key and the D Major key rather than C Major key. For the F Major and G Major key, the number of sharps and flats being the same (6 sharps or 6 flats), it will be the preference of the composer.

However, very often there are modulations (ie changes of keys) within a song. Thus, it will be much simpler for the composer as well as the performer to read or write a modulating passage in C Major when the initial key of the work is G Major or D Major because there is only one or two flats of difference. On the other hand, going from D Major to F Major is much more complex, because you have to remove all the flats and add 6 sharps. Although the latter option is possible, it is less relevant and less logical than the first. On the sharps side, we will find the same logic. It is easier to modulate from F Major to C Major than to modulate from F Major to D Major.

To conclude, we rarely meet works whose initial key signature is a 7-sharps or 7-flats one, but it is possible to meet them along the way, in a piece, hence the importance of knowing them.

There are even some works where we meet keys beyond 7 sharps or 7 flats. We can actually continue the circle on one side or the other by adding more sharps or flats. We then obtain keys with double-sharps or double-flats! This is the case, for example, with the Prelude III of the first book of the Well-Tempered Clavier by J.-S. Bach, whose main tone is C Major, and which modulates especially in E minor (relative key of G Major, is the enharmonic key of A Major). Do not be afraid of such an example, it was for Bach to demonstrate the possibilities of equal temperament and for us to push through the logic of the circle of fifths. :-)

How to rebuild it

Building the circle of the fifths implies first and foremost that you have understood how it works.

Do not try to learn the circle of fifths by heart! The important thing is to understand the mechanics that governs it. Once it is well assimilated, rebuild it will seem a breeze.
Practical exercise: building the circle of fifths

Take a sheet music paper and a pencil.

  1. Start by writing the C Major key and its signature at the top of the sheet.
  2. Then write all the keys starting with the sharp key signatures clockwise, then the flat key signatures in the opposite direction, following well the series of sharps and flats. Make sure the 6-sharp and 6-flat key signatures meet at 6 o'clock (and that the 5-sharp / 7-flat and 7-sharp / 5-flat signatures meet respectively at 5 and 7 o'clock). If you are unfamiliar with sharp and flat series, it's time to review them!
  3. All you have to do is enter the key name of each key signature. Start with the major keys first. There are two ways to do this: either you use the signature to deduce the major key (see the course on key signature), or you start from C and you advance by perfect fifth (going up on sharp key signatures and going down on flat key signatures).
  4. Finally, you can add minor relative keys to complete your circle of fifths. Keep in mind that the minor relative key is a minor third lower (1 and a half tone) than the major key.
All you have to do is check your circle by comparing it to the one on this page.

To lighten your circle, you can use the abbreviations "M" for "Major" and "m" for "minor" to write your keys. You can also simply indicate the number of sharps or flats in the signature rather than writing the signature in its entirety, provided you are sure of the constitution of each signature!

Last update on 2021/05/07

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